-temperature dependence and activation of cellulose solutions Tatiana Budtova, Patrick Navard

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Tatiana Budtova, Patrick Navard. Viscosity-temperature dependence and of cellulose solutions. Nordic Pulp and Paper Research Journal, 2015, Special Issue on Cellulose dissolution and regeneration: systems and interactions, 30 (01), pp.99-104. ￿10.3183/NPPRJ-2015-30-01-p099-104￿. ￿hal-01139845￿

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Special Issue: CELLULOSE DISSOLUTION AND REGENERATION: SYSTEMS AND INTERACTIONS Nordic Pulp & Paper Research Journal Vol 30 no (1) 2015 Viscosity-temperature dependence and activation energy of cellulose solutions Tatiana Budtova and Patrick Navard KEYWORDS: Cellulose, Solutions, Rheology, initially written by De Guzmán (1913), and then Viscosity, Temperature dependence, Activation energy developed by Eyring (1935; 1936): SUMMARY: The dependence of cellulose solution shear η=A exp(Ea/RT) [1] viscosity as a function of temperature and measurements where  is the viscosity, A a constant, Ea the activation of solution activation energy are reviewed based on energy, T the absolute temperature and R the results obtained in our laboratory and elsewhere. per . There is no negative sign in front of Ea since Cellulose is not easy to solubilize. Solutions are often this equation is derived from viscosity, not from the rate forming aggregates and are not stable in time and with of the phenomenon as in the original Arrhenius equation. temperature variations. This can be highlighted by the Eq 1 can be derived from simple thermodynamic calculation of the activation energy of the shear viscosity, considerations where flow is seen as a local transition of a parameter which is very sensitive to any change in the a or a group of between one state state of the solution during the shear experiments. (position before flowing) to another (position after flow Changes in the organization of the solution like gelation occurred) having to overcome an energy barrier. One of or cellulose or solvent degradation are phenomena which the most common models assumes that the flow is are strongly influencing the values of activation energy. controlled by the presence of free volume enabling Cellulose solutions in three classes of solvent, ionic molecules to jump from one place to another. Such liquids, N-methylmorpholine-N-oxide-monohydrate and mechanism implying a relation between free volume and (7-9)% NaOH-water with and without additives, were viscosity was first found empirically by Batschinski analyzed. Cellulose was of various molecular weights. (1913). For small molecules where forces resisting flow The plot of the reduced activation energy versus cellulose are mainly linked to interaction forces, there is a good concentration shows that most points fall within a narrow correlation between Ea and the heat of vaporization at range of values, with a low downward curved shape, not temperatures where there are a large fraction of free in agreement of the predictions developed for flexible volume (Vinogradov, Malkin 1980). For polymers, in chains in semi-dilute regime. addition to overcoming attractive forces, chain entropic ADDRESSES OF THE AUTHORS: Tatiana Budtova considerations are playing an important role. The ([email protected]) and Patrick extensive research activities in the years 1945-1970 on Navard ([email protected]): MINES the rheology of polymers lead to a good experimental ParisTech, PSL Research University, CEMEF - Centre de picture of the applicability of Eq 1. The first conclusion is mise en forme des matériaux, CNRS UMR 7635, CS that this relation is only valid over a limited range of 10207 rue Claude Daunesse 06904 Sophia Antipolis temperatures. As soon as the temperature interval over Cedex, France which Ea is calculated exceeds a certain temperature Corresponding authors: Tatiana Budtova and Patrick range (in the order of an interval of 50°C in most cases), Navard the relation between the Newtonian viscosity and 1/T is not linear anymore. The flow of a polymer is a complex process which has One interesting point is that Ea is independent or is a been widely studied and modeled taking into very weak function of molar mass above a certain mass consideration physical structures at all scales, from the (Fox, Flory 1948). The classical explanation is that only a molecular arrangement of the chain and its local fraction of the whole chain (a segment composed of a movements to large scales features like how chains are certain number of monomers) is the relevant length scale able to move over long distances and how they may interact. Many theories flourished over years with more for the flow of polymers (Kauzmann, Eyring 1940; Ventras, Duda 1977). Such consideration was thus used or less success. There is now a reasonable understanding to explain why the activation energy of linear polymers is of the motion of polymer chains in the dilute and increasing with molar mass up to a saturation point where concentrated/melt states, with still some difficulties in the it is nearly independent of molar mass. Some authors semi-dilute region of polymer solutions since correlation fluctuations are large. In this region, both polymer- used this hypothesis to estimate the mass of this segment, which was suggested to be of the same magnitude as the polymer and polymer-solvent interactions must be taken mass between two entanglement points (Landel et al. into account. With polymer flow processes being 1957). kinetically controlled, the way how flow is influenced by The influence of the molecular structure of polymer temperature has been studied from the start of polymer chains on the value of the activation energy Ea was rheology. Since the easiest experimental set-up to be used is simple shear, the dependence of the shear viscosity of a investigated by many authors. Since Ea is expressing the difficulty of moving the chain from one position to polymer fluid with temperature has been quickly found to another, the intensity of interchain interactions, the be in the general form of the Arrhenius-type (Eq 1), presence, bulkiness and rigidity of side chains are parameters influencing the absolute value of Ea in the

99 Special Issue: CELLULOSE DISSOLUTION AND REGENERATION: SYSTEMS AND INTERACTIONS Nordic Pulp & Paper Research Journal Vol 30 no (1) 2015 molten state. Increasing the size of the side groups is dependence on concentration in the low concentration strongly increasing Ea (Porter, Johnson 1966). In the region can also be found as for solutions of linear and same way, Ea of hyperbranched polymers increases with branched polystyrene in various solvents, increasing generation number (Nunez et al. 2000). chloronaphtalene, alkylnaphtalene and dimethylphtalate Rigidity is also affecting the value of Ea. For example, (Yasuda et al. 1981). polyethylene melt has an activation energy of 30 kJ/mol As can be seen from the review above, most of the (Berry, Fox 1968) while polystyrene has Ea=92 kJ/mol extensive experimental studies were performed before (Spencer, Dillon 1948) and cellulose acetate butyrate 254 1980, after which a lot of progress was made to kJ/mol (Besson, Budtova 2012). Since a part of the understand polymer statics and dynamics. The major activation energy is used for moving from one empty advances were in the semi-dilute regime. The standard space to another, the proximity to model (“blob” theory) assumes that under a certain length temperature Tg is strongly influencing Ea in the molten scale, hydrodynamic interactions must be taken into state. The higher Tg is, the higher Ea will be since account, while they are screened above this critical length viscosity is usually measured in the same temperature scale (Heo, Larson 2008; de Gennes 1979). The polymer interval (Wang, Porter 1995). Blending is also affecting diffusion coefficient depends on the correlation length in the magnitude of Ea, as for example blends of the semi-dilute regime . This length is proportional to polypropylene and ethylene-octene copolymer where Ea the polymer concentration C3/4 (in good solvent) and C1 is increasing with increasing the weight fraction of the in  solvents (Doi, Edwards 1986, Fujita 1990). As a copolymer (McNally et al. 2002). consequence, depending on solvent quality, the activation The temperature dependence of the viscosity of polymer energy would depend on polymer concentration with solutions has also been examined in details in the past. In either an upward curved or a linear shape. As shown in addition to all the molecular features described above for the examples above, this is not always the case, due to polymer melts, the value of Ea is influenced by possible changes in rigidity of the chain with temperature considerations of free volume, quality of solvent, polymer which brings divergence from Eq 1 (ln  being non-linear hydrodynamic parameters, of specific behavior of as a function of 1/T) or possible changes in polymer solvents (as it will be shown for the case of cellulose solution structure and thus difficulties for estimating a dissolved in ionic liquids) or by possible changes in the value of activation energy. structure of the solution upon increasing temperature (as The purpose of this work is to review the values of will be seen for cellulose solutions in NaOH-water which activation of cellulose solutions obtained in our are gelling). The large amount of published data on laboratory with different cellulose sources, molar masses flexible chain polymers in solutions is not giving a clear, and solvents, compare the results with the few published unified picture of the variation of Ea versus polymer data and check the validity of the measurements. concentration. As soon as the molar mass is large, the contribution of the polymer chain to the energy needed to Materials and methods flow is larger than the one of the solvent and Ea is Cellulose solutions increasing with polymer concentration. But the way it is Cellulose solutions have been prepared from various increasing depends on the polymer structure and on the cellulose sources and with various solvents. The origins polymer-solvent interactions. For example, for polyvinyl of cellulose and solution preparations are given in details acetate dissolved in two good solvents (Ferry et al. 1951), in the corresponding papers (references in Table 1) from the Newtonian viscosity dependence on temperature where the activation energy of the viscosity has been gives a linear increase of Ea with polymer concentration, extracted. Wood pulps (WP), bacterial cellulose (BC), with a slope being larger for the better solvent. A detailed spruce sulphite and wood pulp and microcrystalline study of solutions of polyisobutylene in four solvents cellulose (MCC) were used. Table 1 is giving details (toluene, iso-octane, carbon tetrachloride and cyclo- about the cellulose samples and solvents used. hexane), from the dilute state to the melt, shows the Solutions were prepared with three families of solvents: following behavior of Ea versus polymer concentration ionic liquids, NMMO monohydrate and (8-9)%NaOH- (Tager et al. 1963): from very low concentrations up to water. The main preparation features are as following. about 40%, Ea is increasing from the value of Ea of pure - In ionic liquids: two ionic liquids were used, EMIMAc solvents (a few kJ/mol) in a downward curved manner and BMIMCl. They can dissolve cellulose up to a rather and then the slope is changing with an upward increase high concentration (25%) without activation. Cellulose until reaching Ea for the polymer melt at 67 kJ/mol. The must be dried in vacuum prior to dissolution. EMIMAc or change of slope at high concentration is attributed by the BMIMCl and cellulose were mixed in a sealed reaction authors to a change of type of flow, compatible with the vessel and the mixtures were stirred at 80°C for at least reptation approach developed later (Doi, Edwards 1986). 48 h to ensure complete dissolution. Solutions were In the low concentration region (which is of interest for stored at room temperature and protected against the study of cellulose solutions we consider here), Ea moisture absorption. values of the polyisobutylene solutions versus - In NaOH-water: NaOH-water mixture was first cooled concentration are curved downwards and the absolute down to -6°C while cellulose is left in water at +5°C for value of Ea is depending on the solvent, which in this 1-2 h in order to swell. The cold NaOH-water solution case are all good solvents. From chain flexibility was added to this swollen-in-water cellulose and the considerations, these authors show that Ea is higher when mixture was stirred at about 1000 rpm for 2 h at -6°C. the chain flexibility is lower. Upward curved Ea

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Table 1 - Cellulose and solvents studied in our laboratory and varied from 0.001 to 1000 s-1. Ionic liquids are used to calculate the shear viscosity activation energy. EMIMAc hygroscopic and water decreases their viscosity and is 1-ethyl-3-methylimidazolium acetate, BMIMCl is 1-butyl-3- lowers their dissolution efficiency. To prevent water methylimidazolium chloride, NMMO is N-methylmorpholine N- vapors to enter the solution during measurements through oxide monohydrate. the gap, a thin film of low-viscosity silicon oil was placed Name Description Solvent used Reference around the edges of the measuring cell. In other cases, for MCC Microcrystalline BMIMCl and Sescousse et example in the case of some NaOH-cellulose solutions, 170 cellulose EMIMAc al. 2010 rheological experiments were performed using a stress- DP 170 controlled rheometer with a Couette cell geometry. MCC- Microcrystalline 9%NaOH-water Roy 2002 Rheological results and activation energy obtained in 230 cellulose our laboratory will also be compared with the ones DP 230 available in literature, for solutions of wood pulp DP 474 WP- Steam 8%NaOH- Egal 2006 in EMIMAc (Duan et al. 2011), cotton linter in NaOH- 342 exploded pulp 0.7%ZnO-water thiourea-urea-water (Zhang et al. 2011), wood pulp of DP DP 342 1180 dissolved in NMMO monohydrate (Kim et al. 1999), wood cellulose DP 755 in NMMO mixtures MCC- Microcrystalline BMIMCl Sescousse et (Rozhkova et al. 1987) and cotton linters in NaOH- 170 cellulose al 2010 thiourea-water (Ruan et al. 2008). DP 170 MCC- Microcrystalline EMIMAc Gericke et al. Results and discussion 300 cellulose 2009 DP 300 Activation energy measurements as a way to detect WP- Wood pulp of NMMO Blachot et al. solution state anomalies 600 unknown origin 1998 As was detailed in the introductory part, shear flow of DP 600 activation energy of a one-phase polymer solution has WP- Spruce sulphite EMIMAc Gericke et al. several characteristics: the viscosity is decreasing with 1000 pulp, DP 1000 2009 increasing temperature, the activation energy of the BC Bacterial EMIMAc Gericke et al. solution is higher than the one of the solvent and it is cellulose, DP 2009 increasing with increasing concentration. However, 4420 looking at some activation energy results reported in literature for cellulose solutions, these characteristics are Then, the solution was removed from the bath and stored not always found. It must be said that if all experiments at +5 °C. are done carefully (ensuring, for example, that there is no - In NMMO-monohydrate: cellulose is soluble in polymer concentration change in the course of mixtures of NMMO and water in a rather narrow experiment, no flow instability or no solution sliding over temperature and NMMO concentration range. The the walls), the geometry of the measuring cell does not preparation of solutions in NMMO needs to start with a influence the values of viscosity measured and thus the hydrated NMMO-water solution (40-50% of NMMO) values of the activation energy calculated. Three classes where cellulose is swollen. Dissolution occurs while of solvents have been particularly studied due to their slowly heating up to about 120°C and removing water by potential for giving real solutions (no derivatisation vacuum pumping until reaching a monohydrated state of occurring) and offering the possibility to process the solvent, at 13.3% (Navard, Haudin 1981). Addition of cellulose solutions in order to make fibers, films, an antioxydant like propylgallate is compulsory to avoid membranes, aerogels and sponges (see chapters 6, 7, 9, a strong decrease of molar mass and the production of 11 and 12 in Navard 2013). These three classes are degradation products which are dangerous (Rosenau et al. imidazolium-based ionic liquids, NMMO-monohydrate 2002). Solutions are in a liquid phase above a certain and (7-9)%NaOH-water with or without additives. Shear temperature which depends on concentration and must be flow activation energy data are, to the best of our kept below about 120°C to avoid hazardous exothermic knowledge, only available for these three classes of events. solvents. Despite these solvents are considered as good, with one of them (NMMO) being under industrial Rheology exploitation and for ionic liquids having a promising Rheological measurements were all performed in steady future, their cellulose solutions are somewhat state mode in the linear regime in order to measure the complicated and this may lead to inconsistencies in Newtonian viscosity as a function of temperature, from rheological measurements. A review of literature shows which the activation energy is calculated from eq 1. the following features regarding Ea data: Three set-ups have been used, depending on the cellulose - Kim et al. (1999) performed a rheology study of solutions: cone and plate, plate and plate or Couette concentrated cellulose solutions in NMMO monohydrate, geometry (two concentric cylinders). The details can be with cellulose concentration between 15 and 25%. found in the papers referenced in Table 1. For example, Experiments were performed with a capillary rheometer, in the case of ionic liquids, experiments were done with a at a shear rate of 50 s-1. In the reported graphs showing rheometer equipped with plate-plate geometry and a ln(viscosity) as a function of 1/T (see eq.1), very low Ea Peltier temperature control system. Shear rates were values were obtained, from a few kJ/mol to about

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10 kJ/mol, much below the one of the solvent, 45 kJ/mol even if at a given measuring time the measurement of (Navard 1982). viscosity is performed correctly from a rheological point - Another report with a similar solvent, a mixture of of view, the comparison between different temperatures NMMO, dimethylsulfoxide and water (Rozhkova 1987) or concentrations will lead to inconsistencies. Such a gives negative Ea values (below -30 kJ/mol) for cellulose phenomenon can occur, for example, for cellulose concentrations around 1-8%, implying that the viscosity solutions in NMMO monohydrate which are known to is increasing with increasing temperatures which is not very strongly degrade cellulose if no antioxidant is added, the case for cellulose-NMMO solutions. as in Rozhkova 1987. This can be one of the reasons of - Negative values (Ea = -16 and -30 kJ/mol) were also extremely low values of Ea, below the one of un- reported in Ruan et al. 2008 for 4% cellulose dissolved in degraded solvent. Other reasons can also be that at these NaOH-thiourea-water when the temperature was above high concentrations of cellulose (25%), it is not 0°C and above 20°C, respectively. At lower temperatures molecularly dispersed anymore, providing that this ideal (from -5 to 0°C), Ea is positive but with a very high dispersion state can be reached (Fink et al. 2001). value, in the range of 181 kJ/mol, much larger than other Combinations of such factors can thus lead to reported values of cellulose dissolved in NaOH-water measurements of a parameter called “viscosity” which (Roy et al. 2003; Egal 2006, Gavillon 2007, Roy 2002) , reflects different states of solution depending on the NaOH-urea (Gavillon 2006), NaOH-ZnO (Egal 2006) or temperature, mixing state and organization, molecular NaOH-urea-thiourea (Zhang et al. 2011) where Ea is weight distribution and presence of degradation products, around 20-30 kJ/mol for similar cellulose concentrations. rendering results difficult to be interpreted and compared. - Deviations from straight lines in ln(viscosity) versus Another aspect to be taken into consideration for the 1/T can be seen in the case of cellulose-ionic liquid calculation of the activation energy is linked to the way solutions (Gericke et al. 2009; Sescousse et al 2010). viscosity measurements are conducted. The viscosity of a To understand why reported results are showing data fluid is never directly measured; it is a calculated value which look either inconsistent or very different from what which is coming from mechanical measurements like theories would predict, some considerations regarding the torque and velocities of moving parts in the case of state of the solution and viscosity measurements are rotational rheometers. A condition for having a needed. It is possible to calculate the activation energy Ea meaningful viscosity value is thus that the hypothesis of a polymer solution from shear viscosity data only made for deriving the equations used for calculating the when several conditions are fulfilled. A first request is viscosity are obeyed by the measured fluid. For example, that the cellulose-solvent system must be a one-phase the fluid must be laminar without any instability, in fluid solution. This is not such a straightforward particular at the edges of the rotating parts. A meaningful condition for cellulose solutions. For example, it is Ea calculation must also ensure that the flowing fluid is known that solutions of cellulose in NaOH-water are always in the linear regime, in order to measure the so- gelling with its kinetics depending on temperature, called Newtonian viscosity. Polymer chains have the concentration and presence of additives like urea, capacity to orient and change their conformations during thiourea or ZnO (Roy et al. 2003; Cai, Zhang 2006; Ruan flow. Thus, above a certain shear rate related to the et al. 2008; Liu et al. 2011). For example, a 4% cellulose- relaxation processes of the polymer chain and to the 8% NaOH-water solution is gelling in more than 2 days polymer-solvent friction, the viscosity will decrease. If at 5°C, in 23 hours at 20°C and in 6 min at 30°C. In the parts of the measurements are made within this shear same solvent, a 6% cellulose solution is still gelling in thinning regime, the results cannot be exploited in terms more than two days at 5°C, but is gelling in 15 mn at of activation energy. This may be the reason why some 20°C and in a few seconds at 30°C (Liu et al. 2011). Ea data are difficult to understand, as the ones reported in These measurements of gelation time were performed by Kim et al.1999 or in Rozhkova 1987. oscillatory rheological measurements. Since the A last factor is the fact that some solvents are not calculation of Ea requires collecting viscosity data over a showing a straight line when plotting ln(viscosity) versus reasonably large range of temperatures, the risk to reach 1/T, which is of course rendering the calculation of the the gelation region is very high. If viscosity data are activation of the solutions very imprecise. This is the case collected from gelation region, the viscosity of the of imidazolium-based ionic liquids; EMIMAc and solution increases with temperature increase, leading to BMIMCl show a concave dependence of the logarithm of negative Ea values. This is probably the case for data viscosity as a function of inverse temperature (Gericke et reported in (Ruan et al. 2008). Very high values of Ea al. 2009; Sescousse et al. 2010). The concave shape is obtained by Ruan et al. 2008 at temperatures around -5°C kept for cellulose dissolved in these solvents. If making are most probably due to the beginning of water freezing the same plot but for the relative viscosity, straight lines leading to a strong increase of viscosity (Egal et al. 2007; were found indicating that the reason of non-linearity Egal et al. 2008). Another problem is that for trying to comes from the solvent properties and not from dissolved avoid solution gelation, viscosity must be measured over cellulose. The activation energy calculated from the a very narrow temperature and concentration range. This linear approximation of the concave-shaped data can be may be the reason why in (Roy et al. 2003), Ea is not then used only if comparing the results obtained in the seen depending on cellulose concentration. same temperature interval. A second request for calculating Ea is that the solution As can be seen, the activation energy is one of the must not change its organization or its structure either as methods able to detect if viscosity measurements are a function of time or of temperature. If this is the case, meaningful or not. Too low, too high or negative values

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cellulose samples, with a small variation as a function of molar mass and solvent. There is one exception, bacterial cellulose, for which Ea at the highest concentration departs from the general trend. The difficulty to produce well dispersed solutions with high concentrations of this polymer is not allowing clarifying this point. Conclusions Changes in the organization of cellulose solutions like gelation, cellulose degradation or aggregation or shear thinning are strongly influencing the behavior of the solution during shear, an effect to which activation energy is highly sensitive. These phenomena must thus be avoided. Fig 1 - Reduced activation energy of the shear viscosity of The three classes of solvent used (ionic liquids, N- cellulose solutions in different solvents versus cellulose methylmorpholine-N-oxide-monohydrate and NaOH- concentration. Dashed line corresponds to a linear water with and without additives) give values of the approximation with the slope 2.4. The notations are detailed in activation energies which are within a rather narrow Table 1. range for cellulose of more or less comparable DP. The are the signs that the state of the solution is changed plot of the reduced activation energy versus cellulose either due to the flow, as it may occur when entering non- concentration has a low downward curved shape, not in linear regimes, or to thermodynamic or kinetic agreement of the predictions available for flexible chains phenomena. in semi-dilute regime. This may be due to the fact that chains have some rigidity. Shear flow activation energy of cellulose solutions as a function of cellulose concentration Literature A compilation of the viscosity versus temperature data Batschinski, A.J. (1913): Untersuchungenüber die obtained in our laboratory in such a way as having at best innereReibung der Flussigkeiten, Z. Phys. Chem. ,84, 643-706. avoiding all the difficulties described in the above section Berry, G.C. and Fox, T.G. (1968): The viscosity of polymers allows to plot the reduced activation energy Ea-Ea0 and their concentrated solutions, Adv. Polym. Sci., 5, 261-357. versus cellulose concentration where Ea0 is the activation energy at zero cellulose concentration (Fig 1). Besson, F and Budtova, T. (2012): Cellulose ester-polyolefine A first comment regarding Fig. 1 is that despite a few binary blend: Morphological, rheological and mechanical mis-positioned points, most values of Ea-Ea0 are falling properties, Eur. Polym. J., 48, 981–989. in a narrow range of values. Ea-Ea0 is ranging from zero Blachot, J-F., Brunet, N., Navard, P. and Cavaillé, J-Y. up to about 30-50 kJ/mol at concentrations around 15%. (1998): Rheological behavior of cellulose/monohydrate of n- Although values for a single cellulose-solvent couple are methylmorpholine n-oxide solutions. Part 1: liquid state, Rheol. slightly downward curved, we can draw an approximate Acta, 37, 107-114. straight line which gives an increment of Ea-Ea of about 0 Cai J. and Zhang, L.N. (2006): Unique gelation behavior of 2.4 kJ/mol per %. It is tempting to extrapolate to pure cellulose in NaOH/Urea aqueous solution, Biomacromolecules, cellulose. Using a straight line from the data of fig 1, it 7, 183–189 gives about 240 kJ/mol, of the same order of what is found for molten polymers such as cellulose derivative De Gennes, P-G. (1979): Scalings Concepts in Polymer melt: cellulose acetate butyrate has Ea=254 kJ/mol Physics, Cornell University Press, Ithaca, NY. (Besson, Budtova 2012). As for all polymers, the De Guzmán, J. (1913): Relación entre la Fluidez y el Calor de question here is the meaning of a “mole” of chain, related Fusion, Anales de la Sociedad Española de Fisica y Quimica, to the length of the chain segment involved in the 11, 353-362. process. Another issue is that this extrapolation is Doi, M. and Edwards, S.F. (1986): The Theory of Polymer conducted in the semi-dilute state, where molecules are Dynamics, Clarendon Press, Oxford, University Press, New not densely packed and fully entangled. It means that the York. shape of Ea could bend upwards above a certain Duan, X., Xu, J.X., Li, J., and Sun, Y. (2011): Preparation and concentration, to reach higher values than the ones rheological properties of cellulose/chitosan homogeneous extrapolated from Fig 1. solution in ionic liquid, BioResources, 6(4), 4640-4651. The downward curved shape of the plotted lines is not fully in line with the general predictions for flexible chain Egal, M. (2006): Structure and properties of cellulose/NaOH polymers in semi-dilute solutions. The reasons can be aqueous solutions, gels and regenerated objects, Thèse de multiple, the first one being that theory is not applicable doctorat, Ecole Nationale Supérieure des Mines de Paris, to semi-flexible chains. A last comment about Fig 1 is Sophia Antipolis, France. that if indeed Ea is independent of molar mass, then all Egal, M, Budtova, T., and Navard, P. (2007): Structure of Ea-Ea0 values should be very similar, their difference Aqueous Solutions of Microcrystalline Cellulose/Sodium being only linked to different cellulose-solvent Hydroxide below 0°C and the Limit of Cellulose Dissolution, interactions. Fig 1 shows that it is the case for most Biomacromolecules, 8, 2282-2287.

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